CN111259337B - Heavy debris real-time drop point forecasting method based on statistics - Google Patents
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Abstract
The invention discloses a statistical-based method for forecasting a heavy debris falling point in real time, wherein heavy debris falling area planning and recovery rescue are important components of a carrier rocket execution flight scheme, the current real-time calculation of the heavy debris of the carrier rocket is influenced by various uncertain measurement factors, and the forecasting falling point and an actual falling point have larger errors, so that the reasons for generating the errors mainly comprise carrier characteristic point trajectory information acquisition errors, heavy debris flight information calculation errors, atmosphere retardation calculation errors and motion model calculation errors. The calculation method introduces a big data comprehensive analysis concept, is based on the current situation of spaceflight heavy debris measurement and control, fully utilizes the last emission of precious measured data resources, carries out inversion calculation on the wind resistance and the speed correction quantity influencing the drop point calculation, forms a real-time drop point calculation model based on a statistical principle, and shows that the drop point prediction precision of a new model is higher through the last data verification.
Description
Technical Field
The invention relates to a landing prediction technology after debris separation, in particular to a real-time integral extrapolation drop point forecasting method based on a statistical principle.
Background
Generally, satellite launching is different from manned space recovery tasks, and each sub-level debris is separated and then is not tracked continuously by external measurement equipment, so that initial motion information of the debris cannot be obtained through direct measurement when a drop point is calculated, and is obtained through carrier trajectory information estimation at the separation moment. The reason is that the arrow motion vector is too complex (except for accelerating motion in the direction of shooting, the arrow has vectors such as direction, pitch and roll in the relative motion direction), and the magnitude, direction and action time of the relative force during separation are fuzzy control quantities. Since accurate calculation is difficult, the task can be corrected only by using the empirical mode.
In the drop point calculation, the motion of the spacecraft passive section can be regarded as particle motion, and the flying of the spacecraft passive section is mainly influenced by the earth gravity, the Copenoy force and the air resistance only from the aspect of the principle of the kinematics of the object. The passive section can be divided into a free flight section and a reentry section in terms of different stresses, the spacecraft of the free flight section only moves under the action of the gravity of the earth and the Coriolis force caused by rotation, and the difference between the reentry section and the free flight section only increases the influence of air resistance. The equation of motion is as follows:
in the equation of motion above, the air resistance term: x D
Wherein S M The area of the windward side of the debris, v is the comprehensive velocity of the debris, g 0 For ground acceleration of gravity, rho/rho 0 For the height-dependent air density, it can be obtained by looking up the zone atmospheric density table, C D The air resistance coefficient is obtained by looking up an air resistance coefficient table corresponding to the Mach number, and the value of the air resistance coefficient is related to the velocity of the debris. From the formula, in the actual execution of the task, the accurate value of the area of the windward side of the debris is not easy to acquire, and the air density along with the height is not accurate enough, which are factors causing inaccuracy of the calculation of the atmospheric resistance.
The drop point calculation is a differential equation formed by motion equations, a certain step length is required to be designed for iterative calculation in numerical calculation, and it is very important to select a proper step length.
Disclosure of Invention
In order to solve the above problems, the present invention provides a real-time drop point forecasting method based on historical data statistical inversion. The method specifically relates to debris separation information calculation, atmospheric retardation compensation calculation, unpowered merle acceleration calculation, numerical iteration calculation, and numerical inversion of an atmospheric retardation comprehensive coefficient and correction parameters delta V and delta K based on historical real data.
The method specifically comprises the following steps that (1) during separation point trajectory calculation, the influence of a separation time trajectory as an inflection point is eliminated by adopting one-way high-order least square nonlinear fitting, and meanwhile, in order to further improve the separation time trajectory precision, the wreckage initial motion speed information is corrected; (2) On the basis of a conventional atmospheric resistance model, an index of atmospheric density changing along with the altitude is fitted by using least square through analyzing the distribution rule of the atmospheric density along with the altitude h, and an atmospheric retardation model containing an atmospheric retardation comprehensive coefficient, a Mach number influence coefficient and an atmospheric density index is established by combining the influence of the section, the weight and the Mach number of rocket debris, and meanwhile, the atmospheric retardation comprehensive coefficient is compensated and corrected for further improving the accuracy of the atmospheric retardation comprehensive coefficient; (3) Comprehensively considering the influence of factors such as the gravitational force, the Goldfish force, the air resistance and the like, and calculating the unpowered meteority acceleration; (4) Performing numerical iteration to calculate a drop point, realizing the forecast of the drop point, performing iteration calculation by adopting a 5ms step length 'Runge-Kutta' model, and setting an iteration calculation termination identifier to be generally that the elevation H of the drop point relative to the surface of an earth ellipsoid is less than 500 m; (5) Combining the separation acting force influence and historical experience, designing a value range of correction parameters, wherein the value range of delta V is [2, 15] and the value range of delta K is [0.5,4.5]; (6) And carrying out statistics and inversion on the atmospheric retardation coefficient, the atmospheric retardation correction coefficient delta K and the correction speed delta V based on historical data.
In view of the above, the technical scheme adopted by the invention is that a statistical-based real-time heavy debris drop point forecasting method comprises the following steps:
and carrying out inversion based on the historical data to obtain the optimal correction speed delta V and the optimal correction coefficient delta K.
And acquiring optimal debris separation time information from the telemetry time.
An optimal trajectory is selected from a plurality of trajectories of the vehicle.
Calculating the ballistic information at the debris separation moment, wherein the ballistic information comprises ballistic velocity information and ballistic position information.
And correcting the ballistic velocity information at the debris separation time in the debris separation model according to the optimal correction velocity delta V.
And correcting the atmospheric retardation compensation model according to the optimal correction coefficient delta K.
The atmospheric resistance is calculated.
And calculating the unpowered acceleration according to the unpowered merle acceleration model.
And carrying out numerical iteration according to an iteration algorithm and a time iteration step length.
And judging whether the iteration meets a termination condition, if so, outputting a predicted falling point of the debris, and if not, executing the step of calculating the atmospheric resistance.
The reason for adopting the above technology is that the initial motion information of the debris and the atmospheric resistance cannot be accurately obtained during the drop point calculation.
The beneficial technical effects of the invention are as follows:
1. the complexity and the ballistic characteristics of the motion process of the carrier at the separation moment are fully considered, and the influence of the inflection point of the ballistic at the separation moment is eliminated by adopting the one-way high-order least square nonlinear fitting.
2. And correcting the initial motion speed information of the debris, and further improving the accuracy of the initial motion speed information of the debris.
3. And comprehensively considering various factors, establishing an atmospheric retardation model, and performing statistics inversion on atmospheric retardation coefficients based on historical data.
4. And correcting the atmospheric retardation coefficient to further improve the accuracy of the atmospheric retardation coefficient.
5. And (3) designing the value range of correction parameters (correction coefficient and correction speed) by combining the separation acting force influence and historical experience.
6. And carrying out statistics inversion on the atmospheric retardation correction coefficient and the correction speed based on historical data.
7. And a proper iteration method is designed by combining the calculation precision and the real-time calculation requirement.
8. The invention is easy to realize programming and improves the efficiency and the precision of real-time point calculation.
Drawings
FIG. 1 is a process flow diagram of the present invention.
Detailed Description
In order to better understand the objects, technical solutions and advantages of the present invention, the following embodiments are described in detail with reference to the accompanying drawings:
the real-time drop point forecasting method based on the statistical principle is established on the basis of a conventional motion model, two fuzzy correction amounts are added in a basic calculation model according to a comprehensive error fuzzy calculation theory, and one fuzzy correction amount is used for compensating the speed error between calculation and actual motion; a method for adjusting the relationship between model calculations and actual windage while setting a range to reduce the number of iterative calculations based on the motion characteristics of heavy debris, comprising:
(1) Building remains separation information calculation model
The first step of calculating the debris falling point is to know the trajectory information of the debris separation moment, and then numerical calculation can be carried out according to the acceleration condition. The main reason why the high-order fitting calculation is adopted is that the acceleration of the rocket body is changed greatly before and after the separation of the debris, and the calculation result has larger error if the linear fitting calculation is used. And respectively fitting the model by using the information of the trajectory before and after separation, and finally obtaining the average value by using the two groups of results.
Let y j J =1,2, … … n is (n is the number of polynomial regression fitting paragraph points) the j-th sampling point measurement value of the time series t of the ballistic parameter (including position information and speed information); b j Is y j Polynomial regression coefficients of the sequence; p is the order of the fitting polynomial (2,3,4 … …;), and the solution model is:
B＝(D T D) -1 D T Y (1)
wherein:
b j j =1,2 and … … p are polynomial regression coefficients to be solved, and p is a polynomial order to be solved; t is t i I =1,2, … … n is the time corresponding to the ballistic sequence, y i I =1,2, … … n is the j-th sample point measurement for time series t in the ballistic information.
y＝b 0 +b 1 x+…+b p x p ,p＝2,3… (3)
The formula (3) is a least square nonlinear fitting equation, the separation point time is substituted into the formula to obtain fitting trajectory information, and the order of a fitting polynomial in the simulation calculation of the method is 4.x represents the data fitting time and y represents the fitting value at time x.
Assuming that the velocity and the position information of the debris separation calculated by the model formula (3) are respectively: v 0 ＝(v x0 v y0 v z0 )，P 0 ＝(x 0 y 0 z 0 )。v x0 v y0 v z0 Respectively representing the component of the velocity in the X direction, the component of the velocity in the Y direction, and the component of the velocity in the Z direction, X 0 y 0 z 0 The X-direction component, the Y-direction component, and the Z-direction component of the position are shown, respectively. After adding the compensation correction amount (Δ V), the separation information (only speed compensation, not position compensation according to separation characteristics) is:
in the formula
x d ＝x 0 ；y d ＝y 0 ；z d ＝z 0 。
(2) Establishing an atmospheric retardation compensation calculation model
The atmospheric retardation acceleration vector model has a complex derivation process, indexes such as atmospheric density and wind direction of an airspace in a debris falling process need to be considered strictly, and in an actual task, region general atmospheric density data are often adopted for calculation.
g bx Representing the component of the resistive acceleration in the X direction, g by Representing the component of the resistive acceleration in the Y direction, g bz Representing the component of resistive acceleration in the Z direction, v x Representing the component of the velocity in the X direction, v y Representing the component of the velocity in the Y direction, v z Representing the component of the velocity in the Z direction and V representing the integrated velocity.
Index i d Is a high order fit related to altitude (kilometer) and the fit equation is as follows:
a 1 ……a 8 ，b 1 ……b 6 index coefficients are shown in table 1. h is k Indicating the height.
Parameter k v Is a fit value related to the mach number of the flight of debris.
c v Represents a mach number; k is the comprehensive coefficient of atmospheric retardation.
TABLE 1 index coefficient Table
The compensation coefficient deltak is substituted into the formula (5), thereby forming an atmospheric retardation calculation model with the compensation coefficient.
(3) Building unpowered meteor acceleration model
In the falling process, except the influence of atmospheric resistance, the falling process is influenced by gravitation, wherein the gravitation generally refers to the gravity of the earth and the Copenese force generated by the rotation of the earth, the force has the largest influence in the falling process of the debris, and the calculation model is as follows:
wherein g is xd Representing the component of gravitational acceleration in the X direction, g yd Representing the component of gravitational acceleration in the Y direction, g zd Representing the component of the gravitational acceleration in the Z direction.
The above formula has a mesoscale constant J =0.00108263, u =3.986004415e 14 Is the constant of gravity of the earth, w e =0.000072921151467 rotation angular velocity of earth, radius of earth R e ＝6378245.0。
In the no-power falling debris process, the motion acceleration is composed of two parts, namely gravitational acceleration and atmospheric retardation acceleration, so that the no-power falling debris acceleration model can be obtained by the following formulas (6) and (7):
(4) Iterative calculation method for drop point numerical value
Calculating the falling locus and the falling point of the debris falling trajectory, knowing the initial velocity and the position of the object motion according to the kinematics principle of the object, calculating the velocity and the position of the next moment under the condition that the acceleration can be calculated, wherein the time step is not too large and generally does not exceed 10 milliseconds in integral iterative calculation, the smaller the step in actual calculation is, the higher the iterative calculation precision is, but simultaneously, the resource used for calculation is multiplied along with the reduction of the step, and the calculation requirement and the calculation velocity of a computer are combined to comprehensively determine in actual application (the simulation calculation t takes 5 ms). The iterative calculation formula is shown in formula (9). In combination with the separation acting force influence and historical experience, the value range of delta V is [2, 15], the step length is 0.24, the value range of delta K is [0.5,4.5], and the step length is 1/50.0 in calculation.
Referring to fig. 1, the inversion correction coefficient flow is based on historical data statistics:
1. and historical data collection and arrangement, including actual falling points of the debris, debris separation time, carrier flight trajectory and the like.
2. And designing a delta V value range [2, 15], an iteration step length of 0.24, a delta K value range [0.5,4.5] and an iteration step length of 1/50.0 by combining the influence of separation acting force and historical experience.
3. Designing an iterative algorithm, a time iteration step length, an iteration termination condition and the like.
4. Calculating ballistic information at the time of debris separation.
5. And correcting the ballistic velocity information at the debris separation moment according to the correction step length, judging whether the correction amount exceeds the value range, executing step 11 if the correction amount exceeds the value range, and executing step 6 if the correction amount does not exceed the value range.
6. And correcting the atmospheric retardation coefficient according to the correction step length, judging whether the correction amount exceeds the value range, executing the step 5 if the correction amount exceeds the value range, and executing the step 7 if the correction amount does not exceed the value range.
7. The atmospheric resistance is calculated.
8. Unpowered acceleration is calculated.
9. And carrying out numerical iteration according to an iteration algorithm and a time iteration step length.
10. And judging whether the iteration meets the termination condition, if so, executing the step 6, and if not, executing the step 7.
11. And comparing and analyzing the calculation result with the historical actual drop point.
12. And selecting an optimal correction coefficient.
Forecasting a real-time drop point based on a statistical principle:
1. designing an iterative algorithm, a time iteration step length, an iteration termination condition and the like.
2. And filling the optimal correction coefficient.
3. And acquiring optimal debris separation time information from the telemetry time.
4. An optimal trajectory is selected from a plurality of trajectories of the vehicle.
5. Calculating ballistic information at the time of debris separation.
6. And correcting the ballistic velocity information at the debris separation time.
7. And correcting the atmospheric retardation coefficient.
8. The atmospheric resistance is calculated.
9. Unpowered acceleration is calculated.
10. And carrying out numerical iteration according to an iteration algorithm and a time iteration step length.
11. And judging whether the iteration meets the termination condition, if so, executing the step 12, and if not, executing the step 7.
12. Output debris predicts the drop point.
Claims (7)
1. A statistical-based real-time heavy debris drop point forecasting method is characterized by comprising the following steps:
carrying out inversion based on historical data to obtain an optimal correction speed delta V and an optimal correction coefficient delta K;
obtaining optimal debris separation time information from the telemetry time;
selecting an optimal flight trajectory from a plurality of flight trajectories of the carrier;
calculating ballistic information at the debris separation moment, wherein the ballistic information comprises ballistic velocity information and ballistic position information;
correcting ballistic velocity information at the debris separation moment in the debris separation model according to the optimal correction velocity delta V;
correcting the atmospheric retardation compensation model according to the optimal correction coefficient delta K, wherein the corrected atmospheric retardation compensation model is
In the formula, g bx Representing the component of the resistive acceleration in the X direction, g by Representing the component of the resistive acceleration in the Y direction, g bz Representing the component of resistive acceleration in the Z direction, v x Representing the component of the velocity in the X direction, v y Representing the component of the velocity in the Y direction, v z Represents the component of the velocity in the Z direction, and V represents the integrated velocity;
index i d The fitting equation of (a) is as follows:
a 1 ……a 8 ，b 1 ……b 6 denotes the index coefficient, h k Represents a height;
parameter k v Is a fit value related to the mach number of the debris flight;
c v is Mach number; k is the comprehensive coefficient of atmospheric retardation;
calculating the atmospheric resistance;
calculating unpowered acceleration according to the unpowered meteoron acceleration model;
performing numerical iteration according to an iteration algorithm and a time iteration step length;
judging whether the iteration meets a termination condition, if so, outputting a debris predicted drop point, and if not, executing the step of calculating the atmospheric resistance;
the inversion based on historical data comprises the following steps:
1) Collecting and sorting historical data, wherein the historical data comprises the actual falling point of the debris, the debris separation time and the carrier flight trajectory;
2) Designing a correction speed and a correction coefficient by combining the influence of the separation acting force and historical experience;
3) Designing an iterative algorithm, a time iteration step length and an iteration termination condition;
4) Calculating ballistic information of the debris separation moment;
5) Correcting the ballistic velocity information at the wreckage separation moment according to the correction velocity, judging whether the correction amount exceeds the value range, executing step 11) if the correction amount exceeds the value range, and executing step 6) if the correction amount does not exceed the value range;
6) Correcting the atmospheric retardation coefficient according to the correction coefficient, judging whether the correction amount exceeds the value range, if so, executing the step 5), and if not, executing the step 7);
7) Calculating the atmospheric resistance;
8) Calculating unpowered acceleration;
9) Performing numerical iteration according to an iteration algorithm and a time iteration step length;
10 Judging whether the iteration meets the termination condition, if so, executing the step 6), and if not, executing the step 7);
11 Comparing and analyzing the calculation result with the historical actual drop point;
12 An optimum correction speed Δ V and an optimum correction coefficient Δ K are selected.
2. The method of claim 1, wherein the method comprises: and respectively fitting the ballistic information at the debris separation moment by using the ballistic information before and after separation, and finally obtaining the average value by using two groups of results.
3. The method of claim 2, wherein the method comprises: and the trajectory information fitting adopts unidirectional high-order least square nonlinear fitting.
4. The method of claim 1, wherein the method comprises: the corrected debris separation model is
In the formula: velocity information V at time of debris separation 0 ＝(vx 0 vy 0 vz 0 )，vx 0 vy 0 vz 0 Position information P respectively representing a component of a velocity in an X direction, a component of the velocity in a Y direction, a component of the velocity in a Z direction, and a debris separating time 0 ＝(x 0 y 0 z 0 )，x 0 y 0 z 0 Respectively representing a component of the position in the X direction, a component of the position in the Y direction, and a component of the position in the Z direction, and the corrected velocity information and position information are respectively V d And P d ；
x d ＝x 0 ；y d ＝y 0 ；z d ＝z 0 。
5. The method of claim 1, wherein the method comprises: in the unpowered meteority process of the debris, the motion acceleration is composed of two parts, namely gravitational acceleration and atmospheric retarding acceleration, so that the unpowered meteority acceleration model is
g z ＝(g zx ,g zy ,g zz )
g xd Representing the component of gravitational acceleration in the X direction, g yd Representing the component of gravitational acceleration in the Y direction, g zd Representing the component of gravitational acceleration in the Z direction, g bx Representing the component of the resistive acceleration in the X direction, g by Representing the component of the resistive acceleration in the Y direction, g bz Representing the component of resistive acceleration in the Z direction.
6. The method of claim 5, wherein the method comprises: the calculation model of the gravitational acceleration is
Wherein
In the above formula, J is a Rich constant, u is an earth gravity constant, w e Is the angular rate of rotation of the earth, R e The radius of the earth.
7. The method of claim 1, wherein the method comprises: and combining the influence of the separation acting force and historical experience to design a correction speed delta V and a correction coefficient delta K, wherein the value range of the delta V is [2, 15] and the value range of the delta K is [0.5,4.5].
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